I don't know if this is true generally, but in Minnesota this is not the case, and as a parent of three, I would say it does lead to improvement in some schools

I don't know if this is true generally, but in Minnesota this is not the case, and as a parent of three, I would say it does lead to improvement in some schools. The challenge, however, is what to do about the schools which aren't as good, and this seems to be where the the parallels to free-market competition break down a bit. If you buy crummy goods or services from a crummy business, which then goes out of business, that's a feature. If your kid goes to a crummy school and gets a crummy education, and the school eventually gets closed, that's a bug - at least for your kid (although the net utility for society may be maximized).